I really recommend that you get a copy of Rise Up Singing! Some people call it "the death of folk music," but I prefer to call it "America's fake book." Goodness knows it has the chords to gadzillions of songs, only a fraction of which are really traditional folk songs. Use it as a reference, not as a hymnal.
Also, learn the nature of the particular song circle you are joining. Some are essentially community sings, where most if not all the songs are old chestnuts that nearly everyone knows. At the other extreme are song circles for singer-songwriters, where they can try out works in progress if front of a generally supportive audience. Then there are songle circles that are really jam sessions, where they may be singing but it's the instrumental work that is primary.
Just as important, learn the rules or etiquette. These might be very structured and explicit, or they may be very informal, but in either case they exists. The song circles I like best are the ones where everyone in turn can do one of four things:
1. Lead a song. This means you expect other people will be joining in, both vocally and instrumentally. If it is not a well known song, or if you play a non-standard variant, it is a good idea to run through it one time so everyone is together.
2. Perform a song. This means you expect other people to listen quietly and not join in, unless specifically invited (e.g. to sing the chorus, or to provide a particular instrumental accompaniment). Song song circles strongly discourage the option of performing a song; others welcome it.
3. Request a song. This means aking someone else, either the group as a whole or an individual, to a lead a perform a song that you have picked. A person who leads or performs a song in response to a request still gets his/her own turn when it comes around.
4. That is neither lead, nor perform, nor request a song at the moment, but you reserve the right to do so once everyone else has had a turn and before the circle goes around again.